A318363 Multiplicative with a(prime(i)^k) = prime(k)^2^(i-1).

1, 2, 4, 3, 16, 8, 256, 5, 9, 32, 65536, 12, 4294967296, 512, 64, 7, 18446744073709551616, 18, 340282366920938463463374607431768211456, 48, 1024, 131072, 115792089237316195423570985008687907853269984665640564039457584007913129639936, 20, 81, 8589934592, 25

Offset: 1

Author

Rémy Sigrist, Aug 24 2018

Keywords

• nonn
• mult

Comments

This sequence has similarities with A048767.

This sequence is injective (all terms are distinct).

This sequence is a permutation of A268375.

Crossrefs

Cf. A005117, A007947, A048767, A048672, A268375.

Programs

Mathematica

Array[Apply[Times, FactorInteger[#] /. {p_, k_} /; p > 1 :> Prime[k]^2^(PrimePi[p] - 1)] &, 27] /. {1, 1} -> 1 (* Michael De Vlieger, Aug 25 2018 *)

PARI

a(n) = my (f=factor(n)); prod(i=1, #f~, prime(f[i,2])^2^(primepi(f[i,1])-1))

Formula

A007947(a(n)) = A007947(A048767(n)) for any n > 0.

a(A005117(n)) = 2^A048672(n) for any n > 0.